How to construct regular polygons

how to construct regular polygons

Constructing a regular polygon with n sides is the same as dividing a circle into n equal parts, and this is the same as finding Cos(2?/n) or Sin(2?/n). Most trigonometric expressions are transcendental, so there was interest in those which are algebraic. Mathematica will attempt to make this Size: 1MB. The easiest regular polygon to construct is a hexagon. To construct a hexagon, use a compass to draw a circle. Now, (keeping the compass at the same exact setting), place the compass point on the circumference and strike an arc on the circumference. Next, place the compass point in the arc just drawn and strike another arc.

We know that a regular polygon is consfruct polygon that has all sides of equal length and all interior angles reuglar equal measure. Lets start with constructing the first regular polygon, the equilateral triangle. First tegular create a sketch. Make polygns that the arc intersects with the previously drawn ray. Without howw the width of the compass, we repeat the previous step. Triangles are congruent because of the SSS theoremso polgons say we only have one solution.

By donstruct the steps described above, we would get two more triangles, four in total. All four of them are congruent, and we see them as one solution to the problem. Construct a triangle if we what to do to get rid of mice the radius of the circumscribed circle.

How to get the other one? First we draw a regulxr by hand. Make the second arc that intersects with the bisector line. Construct a regular pentagon if we know the radius of the circumscribed circle. Construct a regular hexagon if we know the radius of circumscribed circle. This is even easier. How to construct a regular octagon if we know radius of circumscribed circle?

First we construct a square within the given circle with its diagonals following the process described above. Those points are the remaining vertices of an octagon. How to construct a regular decagon if we know radius of circumscribed circle? First we construct a regular pentagon within the given circle following the process described in construction of pentagon. Those points are the remaining cohstruct of an decagon. How to construct a regular dodecagon if we know radius of circumscribed circle?

Just like we did in the last two examples, we can construct regular dodecagon out of a regular hexagon. How to make free website with free domain name bisectors of central angles of a hexagon give us remaining vertices of dodecagon. Necessary cookies are absolutely essential for the website to function properly.

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Twitter response:. Equilateral triangle Lets start with constructing the first regular polygon, the equilateral triangle. Square Example. First, we make a sketch to know the disposition of the points rebular sides. Regular pentagon First we draw a sketch by hand. Regular hexagon Example. How to construct regular polygons octagon Example. Regular decagon Example. Regular dodecagon Example. The Magic Square Learn about the History of pi The number Pi has Regylar downloaded worksheets Ones to thousands What is Mathemania?

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Last Updated: July 23, References. To create this article, 18 people, some anonymous, worked to edit and improve it over time. This article has been viewed , times. Learn more Constructing regular polygons accurately is very significant in geometry and is easy to do. Log in Social login does not work in incognito and private browsers.

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Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article methods. Tips and Warnings. Things You'll Need. Related Articles. Method 1 of Draw a straight line using the protractor. This will be the center line of your circle dividing it into semi-circles.

Mark the center point. Mark a point for each of the successive angles. Join the points marked on the circle with a line segment. If your points are outside of the circle, then simply mark another point along the radial line from the center onto the circle for each point and then join them.

Check to see that the sides are the same length. If they are, you can erase the circumscribed circle. Method 2 of Draw a circle of the desired radius, r. Set your compass to the radius, r , and draw a circle. Be ultra-accurate and triple-check the measurement to ensure that it is as accurate as possible. Start from any point on the circle and mark an arc or line. Don't change the radius of your compass. Mark another arc or line on the circle. Continue the process until the arc or line touches the first point.

Make sure your compass doesn't move! Check to see that the sides are identical in length. If they are, then you're finished. Erase the construction guide lines. With a normal protractor, all you can do is measure extremely carefully. Yes No.

Not Helpful 3 Helpful 8. Not Helpful 5 Helpful Not Helpful 8 Helpful Since none of the polygons you refer to are regular polygons, they cannot be constructed using this method. Not Helpful 2 Helpful 1. Draw nine radii separating the central angles. Mark the points where the radii intersect the circumference.

Draw straight lines between adjacent points on the circumference, and you've drawn a regular nonagon. Not Helpful 3 Helpful 3. Kevin Zheng. Divide degrees by 7 to get an angle of Measure the same angle successively around the circle until you reach the starting point. You should be able to link the points together. Not Helpful 7 Helpful 2. If you're asking about irregular polygons, the answer is no. The circle method works only for regular polygons.

Not Helpful 5 Helpful 1. You would need a protractor, and you would have to locate or be given the center of the semicircle. Draw a diameter from one end of the semicircle to the other.

Then mark off seven Use those angles to draw six radii, which will divide the semicircle into seven equal parts. Not Helpful 1 Helpful 2. Include your email address to get a message when this question is answered. If you use a mechanical pencil, rotate the pencil slightly as you draw.

This will produce a strong, consistent line. Helpful 1 Not Helpful 1. For the final construction, do all of the marks in fine-line black pen, then paperclip a piece of tracing paper to your ink drawing and do the tracing carefully in pen or pencil.

Helpful 1 Not Helpful 0. Submit a Tip All tip submissions are carefully reviewed before being published. Related wikiHows How to. How to. Co-authors: Updated: July 23, Categories: Featured Articles Geometry. Thanks to all authors for creating a page that has been read , times.

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